Bond Energy

If we pass a direct electric current through water containing enough ions to make it a good electrical conductor, it will break down into its constituents: hydrogen and oxygen. Both hydrogen and oxygen gas exist as diatomic molecules so the equation for this chemical reaction is

2H2O -> 2H2 + O2

The prefixes tell us that it takes 2 molecules of water to produce one molecule of oxygen and two molecules of hydrogen. If we decompose 36 grams of water (2 moles), we produce 2 moles of hydrogen gas (4 g) and one mole of oxygen gas (32 g).

In this reaction, covalent bonds between the hydrogen atoms and oxygen atom in water have been broken and new bonds — between the hydrogen atoms in H2 and the oxygen atoms in O2 — have been formed.
This reaction requires the input of energy (electrical in this case). This is because

it takes energy to break chemical bonds

energy is released as chemical bonds form

but in this case the energy released is less than the energy needed.

Bond Energy

For any particular chemical bond, say the covalent bond between hydrogen and oxygen, the amount of energy it takes to break that bond is exactly the same as the amount of energy released when the bond is formed. This value is called the bond energy.

There are many forms of energy:

electrical

mechanical

chemical

but all forms are ultimately converted into heat.
So it is convenient for biologists to measure energy in units of heat.
The unit we shall use most often is the kilocalorie (kcal): the amount of heat needed to warm 1 liter of water 1 degree Celsius.

The kilocalorie is also the unit used to describe the energy content of foods. It is the "Calorie" used on food labels.

It takes a net of 118 kcal to decompose 2 moles of H2O into its elements. Actually it takes more than 118 kcal to decompose the water into its atoms, but some of the energy is given back as the atoms immediately bond together to form molecules of hydrogen and oxygen.

Let's look at the numbers.

The bond energy of the H-O bond is 110 kcal.

The bond energy of H-H bonds is 103 kcal.

The bond energy of the O=O bonds is 116 kcal.

The decomposition of 2 molecules of water requires breaking 4 H-O bonds and thus the input of 440 kcal.

It is now chemical energy stored in the bonds of the hydrogen and oxygen molecules. The energy stored in this reaction is called free energy because it is still available to do work. It is useful to have a symbol for free energy, and we shall use the letter G (in honor of Josiah Willard Gibbs who developed the concept of free energy).

What is free energy?

It is energy that can be harnessed to do work. The water stored behind a dam has free energy. When allowed to fall through a turbine, it can generate electricity (another form of free energy).

But for biologists, the most interesting form of free energy is the energy stored in chemical bonds. It, too, can be harnessed to do work. When you lift a weight, you are using the free energy stored in the bonds of food molecules to run a machine — your skeletal muscles.

The conversion of free energy to work is never 100% efficient. As you contract your muscles, much of the free energy of your fuel is given off as heat. It is no longer free; there is no way you can harness the warmth of your muscles to accomplish biologically useful work.

A change in free energy is depicted by the letter G preceded by the Greek Delta (Δ).

By convention, we indicate the storage of free energy with a plus sign. So, our reaction is expressed:

2H2O -> 2H2 + O2, Δ
G = +118 kcal.

You may have had a chemistry professor ignite a mixture of hydrogen and oxygen. It not, simply accept my word that the result is a dramatic explosion. The equation for this chemical reaction is the reverse of the one we have been studying and is expressed as

2H2 + O2 -> 2H2O

And, as the explosion suggests, this time a release of energy occurs. In fact, the free energy change is once again 118 kcal. This is because it took only 322 kcal to break the H-H and O=O bonds, and 440 kcal were liberated by the 4 moles of H-O bonds that were formed. (The igniting spark provided the initial input of energy; the surplus from the reaction then provided what was needed to get all the other molecules to react.)

We express the fact that energy came out of the reacting system by putting a minus sign before Δ
G.

2H2 + O2 -> 2H2O, Δ
G = -118 kcal.

These chemical reactions may not seem very "biological" to you, but in fact, they are good models for the reactions at the very heart of life itself.

Cellular respiration

It turns out that mitochondria exploit a similar reaction to secure free energy. Mitochondria synthesize water using the hydrogen atoms removed from organic molecules, like glucose, and the oxygen atoms they take in as they respire. The process is called cellular respiration. [Link to discussion of cellular respiration.]

The same equation describes the burning of glucose, and the same amount of free energy is released. But the energy of burning is released as heat, which is of little value to cells. The achievement of mitochondria is their ability to release the energy of glucose in small, discrete steps so that some of the energy can be trapped in ATP.

Photosynthesis

Similarly, photosynthesis involves the decomposition of water molecules with their hydrogen atoms transferred to carbon atoms to make organic molecules like glucose.

The energies of bonds between atoms of substantially different electronegativities tend to be high, e.g., the 110 kcal of the H-O bond. Another important example is the bonds between oxygen and carbon atoms in carbon dioxide, CO2. The carbon atom shares two pairs of electrons with each of the oxygen atoms, and each of these double bonds has a bond energy of 187 kcal (or about 93 kcal for each shared pair of electrons). The larger the bond energy, the more energy is needed to break the bond. Thus bonds between atoms of differing electronegativities are apt to be very strong and stable.

On the other hand, the energies of bonds between atoms of similar electronegativity tend to be smaller. Of course, where the atoms are the same (e.g., O=O, C-C) there is no electronegativity difference and we are not surprised to find lower bond energy values. Each of the shared electron pairs in the oxygen molecule is worth 58 kcal for a total of 116 in each molecule, as we saw above. The bond energy of the C-C bond is 80 kcal. There is a slight difference in electronegativity between carbon and hydrogen, and a bond energy of 98 kcal. The bonds with smaller bond energies are, by definition, easier to break. Thus these bonds are weaker and less stable.

We should also note that the energy needed to break a particular bond, e.g., between carbon and oxygen, may also be influenced by the nature of the other atoms attached to the ones we are interested in. Thus the C=O double bond in carbon dioxide (O=C=O) has a bond energy of 187 kcal, whereas when this bond is found as part of a larger molecule, the value is closer to 170 kcal. Because of these variations, we speak of average bond energies. This table gives average bond energies for some of the bonds that are always being broken and formed in biochemical processes.